1. Field of the Invention
The present invention relates to the field of transmissions, especially of binary symbol transmissions.
2. Discussion of the Related Art
Symbols or data exhibiting two possible values, for example, +1 and −1, are transmitted. After transmission, due to noise, the values of the received symbols distribute around two values, which will be designated as +a and −a.
FIG. 1 shows an example of distribution of the received values. On abscissa axis Ox is plotted value xi of the received symbol. Probability P(xi) of receiving value xi is plotted on ordinate axis Oy. The received values organize according to a curve 1 centered on positive value +a and a curve 1′ centered around negative value −a.
Since the symbol demodulation generally requires accurately knowing values +a and −a, it will be necessary to estimate value a in as accurate a way as possible.
A first conventional method to determine the value of a comprises measuring the root-mean-square value of the signal over several successive symbols xi. The formula providing the estimated value of a, aest, then is:
                                              ⁢                                                                              a                  est                                =                                ⁢                                                                            1                      N                                        ⁢                                                                  ∑                        i                                            ⁢                                              x                        i                        2                                                                                                                                                                    =                                ⁢                                                                            1                      N                                        ⁢                                                                  ∑                        i                                            ⁢                                                                        (                                                      a                            +                                                          n                              i                                                                                )                                                2                                                                                                                                                                    ≈                                ⁢                                                                                                    1                        N                                            ⁢                                                                        (                          ∑                                                i                                            ⁢                                              a                        2                                                              +                                                                                            ∑                                                      n                            i                            2                                                                          )                                            i                                                                                                                              (        1        )            in which ni represents the noise affecting value xi and N represents the number of symbols.
When the noise is very low, formula (1) provides a value aest equal or very close to +a provided that, as is generally the case, the average value of the noise is zero and the series of values xi is non-correlated with the noise.
Another conventional method to determine the value of +a is to calculate the average of the absolute value of the received values, which results in the following formula:aest=<|xi|>=<|a+ni|>  (2)
This estimate also provides the value of +a in relatively accurate fashion if the noise is not too high.
A problem is however posed for very noisy environments, for example, when noise n is greater than the value of a, as in FIG. 2.
In FIG. 2, curve 2 shows the distribution of the received values xi corresponding to the sending of a positive symbol. Curve 2 exhibits a maximum A for value x=+a and exhibits two portions At and Au on either side of point A. In FIG. 2, the noise is greater than in FIG. 1 and curve 2 cuts ordinate axis Oy at a point C. Portion Cu of curve 2 corresponds to negative received values, while they correspond to positive sent symbols. For portion Cu of curve 2, the received values are affected with a noise greater than a.
Curve 2′ shows the distribution of received values xi corresponding to the sending of a negative symbol. Curve 2′ exhibits a maximum B for value x=−a and two portions Bv and Bw on either side of point B. Curve 2′ cuts ordinate axis Oy at point C.
For an area 3 limited by the abscissa axis and curve portions Cu and Cv, any received value xi may correspond either to a positive sent symbol (point P), or to a negative sent symbol (point Q). These values are a cause of errors in the above-described conventional estimates, the error increasing as the noise increases.
From a given signal-to-noise ratio, the results provided by the preceding method become unexploitable.